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MATHEMATICS Convergent sequence
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Exercise 25: Calculate the limit
.Solution: In the numerator we exclude such a word before the bracket, after which the exemption in the numerator will be the limits other then +K and - K. We exclude from bracket n!.
In the denominator we exclude such a word before the bracket, after which the exemption in the denominator will be the limits other then +K and - K, and in order to the limit of denominator was distinct to 0. We exclude from bracket n!.
We have
We use the definition of n! ( n! = n * (n-1)* (n-2)* ... * 1!, for n 5 £ , thus n! = n * (n-1)! ) . We have
The sequences
are convergent to 0.
Therefore
.